Each of a and b can take values 1 or 2 with equal probability. The probability that the equation ax2 + bx + 1= 0 has real roots, is equal to
Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then, the probability that a face card (jack, queen or king) will appear for the first time on the third turn is equal to
There are two coins, one unbiased with probaility or getting heads and the other one is biased with probability of getting heads. A coin is selected at random and tossed. It shows heads up. Then, the probability that the unbiased coin was selected is
Lines x + y = 1 and 3y = x + 3 intersect the ellipse x2 + 9y2 = 9 at the points P,Q and R. The area of the PQR is
For the variable , the locus of the point of intersection of the lines 3tx - 2y + 6t = 0 and 3x + 2ty - 6 = 0 is
The locus of the mid-points of the chords of an ellipse x2 + 4y2 = 4 that are drawn from the positive end of the minor axis, is
a circle with centre and radius 1
a parabola with focus and directrix x = - 1
an ellipse with centre , major axis and minor axis
a hyperbola with centre , transverse axis 1 and conjugate axis
A point P lies on the circle x2 + y2 = 169. If Q = (5, 12) and R = (-12, 5) then the QPR is
B.
Given equation of circle is,
x2 + y2 = 169
Its centre = ( 0, 0) and radius = 13
Now, slope of OR =
and slope of OQ =
We know that, angle made by the chord of circle at circumference is equal to the half of the angle made by the same chord at the centre of circle.
A point moves, so that the sum of squares of its distance from the points (1, 2) and (- 2, 1) is always 6. Then, its locus is
the straight line
a circle with centre and radius
a parabola with focus (1, 2) and directrix passing through (- 2, 1)
an ellipse with foci (1, 2) and (- 2, 1)
A circle passing through (0, 0), (2, 6), (6, 2) cut the x-axis at the point P (0, 0). Then, the lenght of OP, where O is the origin, is
5
10
For the variable t, the locus of the points of intersection of lines x - 2y = t and x + 2y = is
the straight line x = y
the circle with centre at the origin and radius 1
the ellipse with centre at the origin and one focus
the hyperbola with centre at the origin and one